Implementation of FCM (Fuzzy C-Means) Clustering Segmentation on MATLAB Platform

This study employs the Fuzzy C-Means (FCM) clustering segmentation method implemented on the MATLAB platform. The approach leverages fuzzy theory and mathematical algorithms, combining the advantages of fuzzy logic with C-means clustering to achieve superior data classification and segmentation performance. The MATLAB implementation typically involves key functions such as fcm() for fuzzy clustering operations, where the algorithm iteratively calculates cluster centers and membership matrices. The core mathematical formulation minimizes the objective function J = ΣΣ(μ_ij)^m * ||x_i - c_j||^2, where μ_ij represents the membership degree of data point i to cluster j, m is the fuzzifier parameter (usually set to 2), and c_j denotes cluster centroids. Key implementation steps include: 1. Initialization of cluster centers using random selection or k-means 2. Iterative updating of membership values and cluster centroids 3. Convergence checking based on centroid movement thresholds 4. Defuzzification to assign final cluster labels The code structure typically incorporates MATLAB's matrix operations for efficient computation of Euclidean distances and membership updates, utilizing built-in functions like pdist2() for distance calculations and array operations for vectorized implementation.